Tootfinder

Norming Sets for Tensor and Polynomial Sketching
Yifan Zhang, Joe Kileel
https://arxiv.org/abs/2506.05174 https://arxiv.org/pdf/2506.…

Norming Sets for Tensor and Polynomial Sketching
This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets, we provide a framework for controlling the sketching dimension for \textit{any} sketch operator used to embed said sets, including sub-Gaussian, fast Johnson-Lindenstrauss, and tensor structured sketch operators. Leveraging norming set theory, we propose a ne…

User-Guided Force-Directed Graph Layout
Hasan Balci, Augustin Luna
https://arxiv.org/abs/2506.15860 https://arxiv.org/pdf/2506.15860

User-Guided Force-Directed Graph Layout
Visual analysis of relational data is essential for many real-world analytics tasks, with layout quality being key to interpretability. However, existing layout algorithms often require users to navigate complex parameters to express their intent. We present a user-guided force-directed layout approach that enables intuitive control through freehand sketching. Our method uses classical image analysis techniques to extract structural information from sketches, which is then used to generate posi…

On Sketching Trimmed Statistics
Honghao Lin, Hoai-An Nguyen, David P. Woodruff
https://arxiv.org/abs/2506.07342 https://arxiv.org/pdf…

On Sketching Trimmed Statistics
We present space-efficient linear sketches for estimating trimmed statistics of an $n$-dimensional frequency vector $x$, e.g., the sum of $p$-th powers of the largest $k$ frequencies (i.e., entries) in absolute value, or the $k$-trimmed vector, which excludes the top and bottom $k$ frequencies. This is called the $F_p$ moment of the trimmed vector. Trimmed measures are used in robust estimation, as seen in the R programming language's `trim.var' function and the `trim' parameter in the mean fun…

When topics of discourse prove difficult to approach, stories can help us on our way. This famed short story about a graceful city with an unexpected abberation helps me reflect on where I want to apply my capacity for writing, sketching and teaching.

https://axbom.com/omelas/

#DigitalEthics

A variable dimension sketching strategy for nonlinear least-squares
Stefania Bellavia, Greta Malaspina, Benedetta Morini
https://arxiv.org/abs/2506.03965 h…

A variable dimension sketching strategy for nonlinear least-squares
We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace varies along the iterations, and two strategies are considered for its update: the first is based solely on the Armijo condition, the latter is based on information from the true Gauss-Newton model.…

This https://arxiv.org/abs/2505.24603 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketches
Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique for multiple problems in data science and machine learning, with applications spanning computationally efficient optimization, coded computing, and federated learning. This operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of Renyi Differential Privacy (RDP), providing a refined pri…

SongBloom: Coherent Song Generation via Interleaved Autoregressive Sketching and Diffusion Refinement
Chenyu Yang, Shuai Wang, Hangting Chen, Wei Tan, Jianwei Yu, Haizhou Li
https://arxiv.org/abs/2506.07634

SongBloom: Coherent Song Generation via Interleaved Autoregressive Sketching and Diffusion Refinement
Generating music with coherent structure, harmonious instrumental and vocal elements remains a significant challenge in song generation. Existing language models and diffusion-based methods often struggle to balance global coherence with local fidelity, resulting in outputs that lack musicality or suffer from incoherent progression and mismatched lyrics. This paper introduces $\textbf{SongBloom}$, a novel framework for full-length song generation that leverages an interleaved paradigm of autore…

On Differential Privacy for Adaptively Solving Search Problems via Sketching
Shiyuan Feng, Ying Feng, George Z. Li, Zhao Song, David P. Woodruff, Lichen Zhang
https://arxiv.org/abs/2506.05503

On Differential Privacy for Adaptively Solving Search Problems via Sketching
Recently differential privacy has been used for a number of streaming, data structure, and dynamic graph problems as a means of hiding the internal randomness of the data structure, so that multiple possibly adaptive queries can be made without sacrificing the correctness of the responses. Although these works use differential privacy to show that for some problems it is possible to tolerate $T$ queries using $\widetilde{O}(\sqrt{T})$ copies of a data structure, such results only apply to numer…

Rounding error analysis of randomized CholeskyQR2 for sparse matrices
Haoran Guan, Yuwei Fan
https://arxiv.org/abs/2506.04208 https://

Rounding error analysis of randomized CholeskyQR2 for sparse matrices
This work focuses on rounding error analysis of randomized CholeskyQR2 (RCholeskyQR2) for sparse matrices. We form RCholeskyQR2 with CholeskyQR2 and matrix sketching in order to accelerate CholeskyQR2 and improve its applicability by compressing the input matrix $X \in \mathbb{R}^{m\times n}$. In many real-world applications, the input matrix $X$ is always sparse. In this work, we follow the model of sparse matrices proposed in \cite{CSparse} and provide an improved rounding error analysis of R…

This https://arxiv.org/abs/2502.13583 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fundamental Bias in Inverting Random Sampling Matrices with Application to Sub-sampled Newton
A substantial body of work in machine learning (ML) and randomized numerical linear algebra (RandNLA) has exploited various sorts of random sketching methodologies, including random sampling and random projection, with much of the analysis using Johnson--Lindenstrauss and subspace embedding techniques. Recent studies have identified the issue of inversion bias -- the phenomenon that inverses of random sketches are not unbiased, despite the unbiasedness of the sketches themselves. This bias pres…